Finding Slope From a Table Worksheet

x	−15	−5	5	15	25
y	16	8	0	−8	−16

−15

−5

−8

−16

x	−1	4	9	14	19
y	−4	−14	−24	−34	−44

−1

−4

−14

−24

−34

−44

x	−3	2	7	12	17
y	−1	−11	−21	−31	−41

−3

−1

−11

−21

−31

−41

x	−1	4	9	14	19
y	−4	−9	−14	−19	−24

−1

−4

−9

−14

−19

−24

x	−1	2	5	8	11
y	−4	8	20	32	44

−1

−4

x	0	4	8	12	16
y	−7	−10	−13	−16	−19

−7

−10

−13

−16

−19

x	−3	−1	1	3	5
y	−2	0	2	4	6

−3

−1

−2

x	0	8	16	24	32
y	−7	3	13	23	33

−7

x	−1	1	3	5	7
y	−11	−1	9	19	29

−1

−11

−1

x	−12	−8	−4	0	4
y	−9	−8	−7	−6	−5

−12

−8

−4

−9

−8

−7

−6

−5

x	1	4	7	10	13
y	2	17	32	47	62

x	0	4	8	12	16
y	−5	−1	3	7	11

−1

Slope and line facts behind every answer key

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Every line on these sheets goes through grid points with whole-number coordinates, so a slope can be counted off the graph square by square. The key is worked out with whole-number arithmetic and every slope is given in lowest terms.

Idea	What it says
Slope	rise over run: the change in y divided by the change in x, m = (y₂ − y₁) ÷ (x₂ − x₁)
Slope-intercept form	y = mx + b, where m is the slope and b is the y-intercept, the point (0, b) where the line crosses the y-axis
Positive and negative	a line that climbs from left to right has a positive slope; one that falls has a negative slope
Zero slope	a horizontal line, y = b: it rises by nothing, however far it runs
Undefined slope	a vertical line, x = a: its run is 0, and nothing can be divided by 0
From a table	pick any two rows: the difference of the y values over the difference of the x values, in the same order
Standard form	Ax + By = C. Put y = 0 to find the x-intercept, C ÷ A, and x = 0 to find the y-intercept, C ÷ B
From a point and a slope	put the point into y = mx + b and solve for b: b = y − mx

A short code sits at the foot of every sheet and of its answer key, so loose pages can be matched. The share link rebuilds that sheet, number for number: a key printed next week still fits the copies handed out today.

How it works

In one table x climbs by 10 while y drops by 8: slope −8/10, or −4/5. This finding slope from a table worksheet opens with 12 such tables, each an x row and a y row of 5 values.

Read the full guide

Three kinds of table, easiest first

x goes up by 1 keeps slopes whole: the slope is the jump between neighboring y values. Even steps, the opening setting, moves x by one fixed amount from 2 to 10, so that jump must be divided. Uneven steps prints 4 pairs with unequal gaps: when x runs −1, 2, 3, 5 and y falls by 6, 2 and 4, each ratio is still −2.

Find the slope from a table worksheet: where it fits in grade 8

Common Core standard 8.F.4 has grade 8 students read the rate of change and initial value of a linear function from a table. The initial value is the y-intercept: tick Ask for the y-intercept too and each table gets a second blank.

Watch for students dividing y by x. It works only for lines through (0, 0), about 1 table in 12.
With the y-intercept ticked, x goes up by 1 always includes x = 0; other settings often make students work back.
Have students test a second pair of columns. Two different answers mean a subtraction slip, never a trick table.

Questions and answers

How do you find slope from a table?

Pick any two columns. Subtract the y values, subtract the x values in the same order, then divide the y change by the x change. Columns (−1, −4) and (4, −14) give −10 ÷ 5, a slope of −2.

Are any of the tables not linear?

No. Every table comes from one straight line, so any two columns give the same slope. All values are whole numbers. Slopes are whole numbers from 1 to 5 or fractions with denominators 2 to 5, either sign, never 0.

How many tables fit on one page?

Choose 4, 6, 8, 10 or 12. Each fits one page of Letter or A4, two tables across, and the key adds a second. Print it, or choose Save as PDF in the print window. Four tables leave most of the page blank for working.

What does the key print for each table?

One line, such as slope −4/5, or slope −2, y-intercept −6 with the intercept box ticked. Fractions are in lowest terms. No working is shown, so have students write both changes beside each table.

Finding Slope From a Table Worksheet With Even and Uneven Steps